No Solution or Any Value of x

[harpazo]

Solve for x.

7(x + 3 ) = 6 - (-7x - 15)

7x + 21 = 6 + 7x + 15

I quickly see that -7x and 7x cancel out leaving us with 21 = 21.

My Answer: NO SOLUTION

However, the correct answer is ALL VALUES OF X MAKE A TRUE STATEMENT HERE. I mistakenly assumed that since x cancels out there is no solution to this linear equation. Why is the answer ANY VALUE of x? Seeking different replies, if possible. We do not all explain math the same way.

 

[Harry_the_cat]

21 = 21 is a true statement no matter what x is. The LHS = 7x + 21 and the RHS = 7x + 21. No matter what you put in for x, they will always be equal.

If, however you came to the conclusion that 21 = 22, obviously that is never true, so there are no solutions for x.
That is, there is no value of x that will make 7x + 21 = 7x + 22.

 

[harpazo]

21 = 21 is a true statement no matter what x is. The LHS = 7x + 21 and the RHS = 7x + 21. No matter what you put in for x, they will always be equal.

If, however you came to the conclusion that 21 = 22, obviously that is never true, so there are no solutions for x.
That is, there is no value of x that will make 7x + 21 = 7x + 22.

In all my years involved with textbooks, I never came across an equation like this one. Thank you for your reply.